1QOLS, Blackett Laboratory, Imperial College London SW7 2AZ, UK
2Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, F-75231 Paris, France
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Abstract
We study different aspects of the stabilizer entropies (SEs) and compare them against known nonstabilizerness monotones such as the min-relative entropy and the robustness of magic. First, by means of explicit examples, we show that, for Rényi index $0leq nleq2$, the SEs are not monotones with respect to stabilizer protocols which include computational-basis measurements, not even when restricting to pure states (while the question remains open for $ngeq2$). Next, we show that, for any Rényi index, the SEs do not satisfy a strong monotonicity condition with respect to computational-basis measurements. We further study SEs in different classes of many-body states. We compare the SEs with other measures, either proving or providing numerical evidence for inequalities between them.
Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. In addition to previously developed exact methods to compute the Rényi SEs, we also put forward a scheme based on perfect MPS sampling, allowing us to compute efficiently the von Neumann SE for large bond dimensions.
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Cited by
[1] Poetri Sonya Tarabunga, Emanuele Tirrito, Titas Chanda, and Marcello Dalmonte, “Many-body magic via Pauli-Markov chains — from criticality to gauge theories”, arXiv:2305.18541, (2023).
[2] Emanuele Tirrito, Poetri Sonya Tarabunga, Gugliemo Lami, Titas Chanda, Lorenzo Leone, Salvatore F. E. Oliviero, Marcello Dalmonte, Mario Collura, and Alioscia Hamma, “Quantifying non-stabilizerness through entanglement spectrum flatness”, arXiv:2304.01175, (2023).
[3] Xhek Turkeshi, Marco Schirò, and Piotr Sierant, “Measuring Magic via Multifractal Flatness”, arXiv:2305.11797, (2023).
[4] Guglielmo Lami and Mario Collura, “Quantum Magic via Perfect Pauli Sampling of Matrix Product States”, arXiv:2303.05536, (2023).
[5] Junjie Chen, Yuxuan Yan, and You Zhou, “Magic of quantum hypergraph states”, arXiv:2308.01886, (2023).
[6] Oliver Hahn, Alessandro Ferraro, Lina Hultquist, Giulia Ferrini, and Laura García-Álvarez, “Erratum: Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [Phys. Rev. Lett. 128, 210502 (2022)]”, Physical Review Letters 131 4, 049901 (2023).
[7] Tobias Haug, Soovin Lee, and M. S. Kim, “Efficient stabilizer entropies for quantum computers”, arXiv:2305.19152, (2023).
[8] Davide Rattacaso, Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, “Stabilizer entropy dynamics after a quantum quench”, arXiv:2304.13768, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-08-29 02:14:22). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2023-08-29 02:14:21).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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